Find the magnitude of acceleration of the puck on the ramp

[ScullyX51]

Homework Statement

A .20 kg hockey puck is launched up a metal ramp that is inclined at a 30.0 degree angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are
M_s= .40 kg and M_k=.30 kg , respectively. The puck's initial speed is 35.0 m/s. What is the magnitude of the acceleration of the puck on the ramp?

Homework Equations

F= ma

The Attempt at a Solution

N= Nj
Fgrav= mg(cos 30- sin 30)
Friction= M_kN

In the j direction the forces are:
N-mgsin(30)=0
N= -1.94
In the i direction the forces are:
mgcos(30) + M_kN=ma
a= (mgcos(30)+ M_kN)/ m =a

then when I plug in all of the given numbers I get -1.4.
I have tried this problem a bunch of times and cannot get anywhere close to the correct answer. What am I doing wrong?

 

[PhanthomJay]

Homework Statement

A .20 kg hockey puck is launched up a metal ramp that is inclined at a 30.0 degree angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are
M_s= .40 kg and M_k=.30 kg , respectively. The puck's initial speed is 35.0 m/s. What is the magnitude of the acceleration of the puck on the ramp?

Homework Equations

F= ma

The Attempt at a Solution

N= Nj
Fgrav= mg(cos 30- sin 30)
Friction= M_kN

In the j direction the forces are:
N-mgsin(30)=0
N= -1.94
In the i direction the forces are:
mgcos(30) + M_kN=ma
a= (mgcos(30)+ M_kN)/ m =a

then when I plug in all of the given numbers I get -1.4.
I have tried this problem a bunch of times and cannot get anywhere close to the correct answer. What am I doing wrong?

mostly you've got your mgsin30 and mgcos 30 mixed up.

 

[thomate1]

I would like to point out that the given data may not be sufficient to accurately calculate the magnitude of acceleration of the puck on the ramp. The coefficient of kinetic friction, Mk, is given in units of kg, which is not a standard unit for friction. It is possible that this is a typo and the correct unit is N/kg, but without confirmation, it is difficult to determine the correct value to use in the equation.

Additionally, the provided value for the normal force, N, is negative, which does not make physical sense. The normal force should always be positive, as it is a force exerted by the ramp on the puck in the opposite direction of the gravitational force.

Assuming the correct value for Mk is 0.30 N/kg, the correct approach to solving this problem would be to first calculate the normal force, N, using the given coefficient of static friction, Ms, and the weight of the puck, mg. Then, use this value for N in the equation for the net force in the i direction, along with the given initial speed and mass of the puck, to solve for the magnitude of acceleration, a.

In summary, to accurately calculate the magnitude of acceleration of the puck on the ramp, we need to confirm the unit for the coefficient of kinetic friction, and use the correct value for the normal force in the calculations.